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Atlas › Integer Profiles › Node 9,972,080

9,972,080

24 × 5 × 31 × 4021
Abundant Even Composite

9,972,080 factors as 2^4 × 5 × 31 × 4021. Its 40 positive divisors give a proper-divisor sum of 13,966,864, so this integer is abundant. The Collatz stopping time is 176 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 31 × 4021
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 23,938,944
Proper Divisor Sum 13,966,864
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #9972059 ← → #9972101

Radix Representation

Decimal 9972080
Binary 100110000010100101110000 (24 bits)
Octal 0o46024560
Hexadecimal 0x982970

Divisor Catalog (40)

1 2 4 5 8 10 16 20 31 40 62 80 124 155 248 310 496 620 1,240 2,480 4,021 8,042 16,084 20,105 32,168 40,210 64,336 80,420 124,651 160,840 249,302 321,680 498,604 623,255 997,208 1,246,510 1,994,416 2,493,020 4,986,040 9,972,080

Collatz Trajectory (176 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

9,972,080 4,986,040 2,493,020 1,246,510 623,255 1,869,766 934,883 2,804,650 1,402,325 4,206,976 2,103,488 1,051,744 525,872 262,936 131,468 65,734 32,867 98,602 49,301 147,904 73,952 36,976 18,488 9,244 4,622 2,311 6,934 3,467 10,402 5,201 15,604 7,802 3,901 11,704 5,852 2,926 1,463 4,390 2,195 6,586 3,293 9,880 4,940 2,470 1,235 3,706 1,853 5,560 2,780 1,390 695 2,086 1,043 3,130 1,565 4,696 2,348 1,174 587 1,762

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